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Inversion layers in silicon on insulating substrates
Surface Science 98 (1980) 427-436 0 North-Holland Publishing Company and Yamada Science Foundation
INVERSION LAYERS IN SILICON ON INSULAT~G
Th. ENGLERT
SUBSTRATES
and G. ~~~~
Hochfeldmagnetlabor Grenoble, France
Grenoble. Max-Planck-Institut fiir Festk&perforschung,
F-38042
J. PONTCHARRA Laboratoire d’Electronique
et de Technologie de I’lnformatique,
CENG, Grenoble, France
and G. DORDA Fors~hungs~borato~.en
der Siemens AG, ~~~~hen,
Germany
Received 20 July 1979; accepted for publication 5 September 1979
Magnetoconductance oscillations in silicon MOSFETs on sapphire and spine1 substrates were studied in magnetic fields up to 20 Tesla. For (100) n-type inversion layers the cyclotron mass and the effective Land& g-factor were determined from a measurement of the temperature dependence and the variation of the oscillatory structure in a tilted magnetic field. Apart from the unexplained valley degeneracy factor of two the results are in good agreement with the conception that due to the built-in stress the I?; subband is occupied. The Land&g-factor obtained is about the same as in MOSFETs grown on bulk material. The occurrence of a beat effect in the oscillations above about 12 Tesla in silicon on sapphire samples can be explained by a splitting of the ground subband of about 1 meV. This effect was not observed on silicon on spine1 samples which favours an explanation based on the stress anisotropy in silicon on sapphire.
1. Introduction
The physical properties of an electron gas in the surface space charge layer of semiconductors have been the subject of considerable theoretical and experimental work during the last years. Silicon field effect transistors (FET) of the MOS-type (Metal-Oxide-Semiconductor) provide a readily available tool for the study of surface quantization which arises from the restriction of the carrier motion in the direction perpendicular to the surface [ 11. Among all possible surface orientations MOSFETs grown on a (100) surface of silicon exhibit the best device characteristics. In the SOS technology (silicon on sapphire or spinel) thin expitaxial layers of silicon on single crystal sapphire or spine1 substrates are used for the fabrication of 427
MOSFETs. Thii technology has been developed in order to improve some device properties, like e.g. the switching time. However, the mobility of SOS MOS devices is in general lower than that of conventional MOSFETs. One reason is the existence of traps at the interface between the insulating substrate and the silicon film. A more fu~damen~l difference, which makes the system attractive from the physical point of view, is due to the presence of large lateral stresses in the silicon film, This stress builds up when the wafers are cooled down from the growth temperature to room temperature. From the different thermal expansion coefficients of silicon and sapphire a stress of 9.2 kbar at room temperature has been calculated 121. Recently we have determined the stress in our devices experimentally using Raman spectroscopy and obtained a value of 8.7 kbar at 77 K. Details of the experiment are described elsewhere [3]. The built-in stress changes the electronic structure of the surface charge layer significantly. In the case of an n-type inversion layer on a (100) silicon surface the six degenerate conduction band minima are split into two quasi two-~ensior~al subband systems Ei and Ej.In the absence of stresses the energetically lowest subband is the E, band which consists of states o~~nating from the two valleys with a large effective mass perpendicular to the surface. The theoreticai cyclotron mass in the Ee band is 0.19 nao. The next higher subband, EA is fourfold degenerate with a mass of 0.42 mo. The energy difference EA - E. is of the order 20 meV depending on the surface electric field strength. In the presence of stresses the E(k) minima are shifted relative to each other. Using the deformation potential constant of bulk silicon one finds that a compressional stress of 8.7 kbar, which is isotropic parallel to the surface, leads to splitt.ing of the E. and EL subband by about 80 meV. As a consequence the energetically lowest subband in the SOS system should be the Eb subband with a valley degeneracy of 4 and a theoretical cyclotron mass of 0.42 PYle. The occupation of the Ek subband could be observed on conventions (100) MOSFETs in measuren~ent of the surface quantum oscitiations of the ShubnikovDe Haas type (SdH) under external unaxial pressure [4] and recently in cyclotron resonance experiments on the same system [5]. The first measurements of SdH oscillations on SOS samples were published by Hatanaka et al. f6]. They reported a measured cyclotron mass varying between 0.3 and 0.4 m. and a valley degeneracy of 4. However, it could be demonstrated in tilted field experiments f7] that the observed valley degeneracy is only two. The effective mass was estimated to be 0.5 m, f 10% f7f. In a more recent pub~cat~on Wakabayashi et al. [8] also reported the observation of a valley degeneracy factor of 2 and an effective mass varying from 0.6 to 0.5 m. for different carrier concentrations. However, in this paper a different alignment of the observed SdH peaks is used and consequently unusually large values for the Land6 g-factor are proposed. Zn order to get additional information we have performed measurements in magnetic fields up to 19.5 T. We have turned the samples in the magnetic field to determine the Land6 g-factor. Since the maximum carrier mobility for SOS devices at
low temperature is only of the order 1000 cm2/V 1s high magnetic fields are indispensable for such experiments. We have studied an interference effect which occurs above about 12 T in silicon on sapphire samples. A comparison is made between the properties of silicon on sapphire and silicon on spine1 devices.
2. Experimentaf Silicon on sapphire samples f(lOO) Sif(iOl2) sapphire) were provided by the Forscl~ungs~borato~en der Siemens AG, Munchen, and by the Laboratoire d’Electronique et de Technologie de l’Informatique, CENG, Grenoble. The samples had a short, broad channel, the oxide thickness was 1200 A. Silicon on spine1 samples {(loo) Si/(lOO) spinel} were provided by Siemens, Miinchen. The thickness of the silicon layer varied from 0.6 to 0.8 pm. The SdH oscillations were ~vestigated using standard DC and AC modula~on techniques for the measurement of the conductivity or its derivative do/d V,
3. Ex~r~entaI
results
3.1. Silicon on sapphire For the measurement of the spin splitting and for a determination of the valley degeneracy it is essential to know the energy level scheme which belongs to the observed oscillatory structure. Since the first experiments of Fang and Stiles 191, the tilted field method has proved to be very succesful for a determina~on of the ratio between spin splitting g&B 4’g: Land& factor, fin: Bohr’s magneton) and the Landau splitting kw, (oc: cyclotron frequency eB[m,). Because of the restriction of the carrier motion essentially parallel to the surface in a quasi two-dimensional system the Landau splitting depends only on the component of the magnetic field perpendicular to the surface whereas the total magnetic field determines the spin splitting. Fig. 1 shows some recordings of quantum oscillations as a function of the gate voltage for different angles 9, r$ being the angle between the magnetic field and the surface normal. In this experiment the magnetic field perpendicular to the surface, BL, was kept constant. When the sample was tilted by an angle Q the total magnetic field Br, was increased so that B1 =Btot cos $ remained constant. In such an exper~ent the spin spotting increases proportions to I/cos $Jwhereas the Landau splitting does not change. A relative maximum of the oscillations is expected when the ratio of spin splitting to Landau splitting gm,/(2wa0 CDScb>= z, z being an integer. In these cases spin split levels of different Landau quantum numbers coincide. A doubling of the SdH frequency and a relative minimum of the amplitude occurs when gm,/f2mo cos @) = z t $; We observed a relative maximum of the
Th. Englert et al. ~~n~e~si~nZayers in .Sion instating ~~st~ntes _~~~~~ ~_.. ---_____- ~~-_
,
SOS EL= 10.5T
8~18.3
T
Fig. 1. Quantum oscillations on a silicon on sapphire device at different tilt angles #_ The magnetic field perpendicu~r to the surface is constant. Fig. 2. Quantum oscillations on a silicon on sapphire device at different tilt angles c$.The total magnetic field is constant.
oscillations at 35” and a minimum at 57” for a carrier concentration of n - 1.5 X 1012 cme2. Fig. 2 shows recordings at higher tilt angles. In this case a constant magnetic field of B = 18.3 T was applied perpendicul~ to the surface. Above about 60” the two Ievels indicated by arrows begin to merge and a second coincidence is observed forqb=65”. From the observation of three consecutive integer or half integer coincidences we obtain PC 2m0 cos 35” =’ ’
mc 2m0 cos 57”
=z+;,
gmC
2m0 cos 65”
=z+l.
The ratio of these values is 1 : 1.50 : 1.94. It follows that z = 1. Therefore the ratio of spin splitting to Landau splitting at @= 0 isgm,/2m0 = 0.82 for a carrier density of pa- 1.5 X 1012 cm-‘. This means that the observed minima in the SdH oscillations of the conducti~ty occur between spin split levels of the same Landau quantum number. Spin split levels of adjacent Landau levels overlap. The Landau level scheme proposed by Wakabayashi et al. [8] uses z = 2 for the first observed coincidence. This is, however, not compatible with our data. The width of the first observed peak is only about half as large on the gate voltage scale as that of the subsequent peaks. This results from the different degeneracy factor of the lowest
Th. Englert et al. /Inversion
layers in Si on insulating substrates
431
level and is consistent with our level scheme OJ, OtlJ, 1?2$ etc. (t, 4 denotes the spin orientation). The valley degeneracy was found to be 1.85 + 10% in agreement with former results [7,8]. The discrepancy between the theoretically expected value of 4 and the experimental results will be discussed later. From the temperature dependence of the amplitude (A) of the SdH oscillations as a function of the magnetic field the cyclotron mass was determined. Using the formula A a T/sinh(2n2kT/Ao,)
,
we obtained the values given in table 1. These values are in agreement with an estimate made in our previous publication [7] and with the data of Wakabayashi et al. [8] in their more recent publication. The relatively large error margin which we assumed will be discussed later. The cyclotron mass is larger than expected from effective mass theory for the EA subband. However, similar mass values have been observed in SdH measurements on bulk (100) MOSFETs under unaxial external stress when the Ei subband was occupied [4]. In recent cyclotron resonance experiments on the same system a value of 0.48 m, independent of the carrier concentration was obtained [5]. The enhanced cyclotron mass in the EA subband has not yet been explained theoretically. From the measurements of gm,/2m0 and the cyclotron mass m, a Land6 g-factor g - 3 is deduced at n - 1.5 X 1012 cme2. This value is comparable to the g-factor obtained in the &, subband. Unexpected interference effects occur above about 12 T when the SdH oscillations are measured as a function of the magnetic field. Fig. 3 shows typical results for the derivative dI/dV, at three different gate voltages. The underived curve is also plotted in the case of V, = 11 V. A rather complicated oscillatory structure is observed when the surface quantum oscillations are measured at a high magnetic field as a function of the gate voltage. This can be seen in the lower part of fig. 4. In fig. 5 the magnetic field position of the SdH extrema are plotted as a function of the gate voltage. The occurrence of the beat effect is indicated by arrows. It is most pronounced at relatively small gate voltages. Only some of the points in fig. 5 lie on straight lines with a common intercept. It should be mentioned that this effect has
Table 1 Cyclotron
mass mJmo
at various electron
n (cme2)
m&no
1.4 2.3 3.5 4.4
0.51 0.49 0.52 0.47
x X x x
10’2 1Ol2 10’2 10’2
(i 10%)
concentrations
n
Th. Englert et al. /Inversion
SILICON
ON
n-channel
SAPPHIRE
layers in Si on insulating substrates
1
(100)
r\
I
I
5
10
I 15 B(T)
Fig. 3. SdH oscillations
SILICON ON SAPPHIRE
I 20 -
on a silicon on sapphire
sample at different
gate voltages.
Fig. 4. Conductivity and field effect mobility for a silicon on sapphire part) and SdH oscillations (lower part) at a constant magnetic field.
sample
at B = 0 (upper
been observed for all our samples investigated even of different origin. Therefore it seems to be an’intrinsic property of the silicon on sapphire system. A possible explanation is the splitting of the ground subband Ei by a small anisotropy of the stress along the surface. Since the surface used for the expitaxy is not a plane of high symmetry, the different thermal expansion parallel and perpendicular to the c-axis of sapphire leads to an anisotropy of about 5% of the total built-in stress [2]. This should give rise to a stress induced valley splitting of about 5 meV. Unfortunately the stress anisotropy has not been determined experimentally up to now. In order to see whether such a splitting can account for the observed interference effect, we have performed a computer simulation by superimposing SdH oscillations from two valleys with slightly different Fermi energies. The SdH formula given by Roth et al. [lo] was employed because the two-dimensional nature of the electron gas was not significant. Use was made of the experimentally determined gm,/2m,, value. For a gate voltage of 11 V we were able to simulate the experimentally observed interference structure with a splitting of AE = 1 meV. Although
I
Th. Englert et al. /Inversion
r
SILICON
layers in Si on insulating substrates
ON
433
SAPPHIRE
20
t m 15
10
5
5
10
15
20
25
30
35
Fig. 5. Extrema of SdH oscillations for a silicon on sapphire MOSFET. The arrows indicate the occurrence of interference effects.
this splitting is considerably smaller than expected from the calculated anisotropy of the stress it can explain the results qualitatively. The interference effect has some consequences for the interpretation of SdH data at lower magnetic fields. Although it can only be resolved above about 12 T it changes the shape and the amplitude of the oscillations at much lower fields. This causes an error in the determination of the effective mass from the temperature dependence of the SdH amplitude using only one fundamental period. In order to estimate this error we have simulated SdH oscillations for Vs = 11 V as described above at various temperatures. For the calculation we used the theoretical mass value m, = 0.43 mo. Then we have recalculated the cyclotron mass from the temperature dependence of the simulated curves using the formula A a T/sinh(2~2kT/Ao,)
.
We found a discrepancy of about 5% between this result and the value inserted in the calculation. Therefore we assumed a rather large error margin for our mass data shown in table 1. 3.2. Silicon on spine1 As for the amount of built-in stress the system (100) silicon on (100) spine1 is very similar to silicon on sapphire [ 111. However, in this case the stress should be isotropic parallel to the film surface because spine1 is cubic. Therefore a comparison
434
Th. Englert et al. j Inversion layers in Si on inflating castrates
1
t
L___
SILICON
ON
SPINEL
I
I
I
I
5
10
15
20
B(T)
--+
Fig. 6. SdH oscillations on a silicon on spine1 sample.
of the properties of MOSFETs grown on the two different insulating substrates is a good check for the model proposed above. Fig. 6 shows the SdH oscillations as a function of the magnetic field for different gate voltages. The extrema are plotted versus gate voltage in fig. 7. As can be seen from the data, there is no anomalous structure in the oscillations. Especially the beat effect which was observed for
20
SILICON
ON
SPINEL
T i= m
5
10
15
20
25 vg w
30 --b
Fig. 7. Extrema of SdH oscillations for a silicon on spine1 device.
Th. Englert et al. /Inversion
layers in Si on insulating substrates
435
silicon on sapphire samples does not exist. This confirms our model that the anisotropy of the stress is responsible for the splitting. We have found another difference in the properties of silicon on sapphire and silicon on spine1 devices. When the field effect mobility of MOSFETs on sapphire substrate is measured at low temperatures (below 80 K) a minimum is observed at a carrier density of about 4.4 X 10” cm -2. This structure has been reported first by Kawaji et al. [ 121 and interpreted as the occupation of the E,-, subband with a small effective mass. However, the energy difference Ee - Eh calculated from the stress values seems to be too large for an occupation at these carrier densities. We observed such a minimum in the field effect mobility on all our sapphire samples. There was no indication for the occupation of another subband in our SdH data. It should be mentioned, however, that the oscillations at high gate voltages are rather weak (see e.g. fig. 5). For our silicon on spine1 samples no such structure in the field effect mobility could be observed. We have no satisfactory explanation for the effect at present but this different behaviour seems to be important for any future interpretation.
4. Discussion and concluding
remarks
We have checked in this paper that the ground state of a (100) inversion layer on silicon on sapphire is twofold degenerate. The cyclotron mass and the effective g-factor have been determined. Apart from the valley degeneracy problem the results are in agreement with the conception that due to the built-in stress the EA subband is occupied. An additional splitting of the subband was detected in the SdH oscillations at high magnetic fields which can be explained qualitatively by the anisotropy of the stress parallel to the surface. This model is supported by the results on silicon on spine1 samples where no such anisotropy exists. In our discussion we have neglected so far the discrepancy between the theoretically expected and the observed valley degeneracy. It should be mentioned that this problem is not limited to the SOS system. It has been a serious difficulty in understanding the physics of surface space charge layers on silicon of the orientation (110) and (111). However, a valley degeneracy of six for specially treated (111) samples was observed recently by Tsui et al. [ 131’. This shows that a valley degeneracy factor larger than two is possible. Since the samples used in that experiment were fabricated in a different way, one has to assume that some property of the interface which is not known up to now leads to the lifting of the valley degeneracy In this paper we have explained the observed splitting of the ground subband in silicon on sapphire devices by the anisotropy of the stress in the surface. Attempts to interpret the beat effect by two periods caused by valley splitting does not seem reasonable for various reasons. First of all, it is difficult to see, how valley splitting can arise, if the “tunneling in k-space” [ 181 or the “surface scattering” [ 191 models
Th. Englert et al. /Inversion
436
layers in Si on insulating substrates
of the valley splitting are invoked. Moreover, the experimentally observed splitting is not compatible with the electric field dependence of the valley splitting as theoretically predicted [ 14-161. The most convincing argument is, however, that the splitting is missing in the silicon-on-spine1 devices, However, the proposed model has some implications. The stress anisotropy can only split those E(k) valleys which are located at right angles in k-space in the stress-free case. If the two occupied valleys were on the same axis. uniaxial stress should have no effect at all. It should be noted that the model of Kelly and Falicov [17] which leads to a reduction of the valley degeneracy is based on the interaction of electrons in valleys perpendicular to each other. At present the charge density wave model [17] could neither be proved nor disproved. One argument against its validity has been the invoked strength of the intervalley electron-electron interaction, which must be much larger than in bulk silicon.
References [l] [2] [3] [4] [5] [6] [7] [8]
[9] [lo] [l l] [12] [13] [14] [15] [16] [17]
See e.g., G. Landwehr, in: Solid State Devices, 1978, Eds. M. Savelli and J.P. Nougier (Les Editions de Physique, Orsay, 1979) p. 1. A.J. Hughes and A.C. Thorsen, J. Appl. Phys. 44 (1973) 2304. Th. Englert and G. Abstreiter, Solid State Electron. 23 (1980) 31. Th. Englert, G. Landwehr, K. van Klitzing, G. Dorda and H. Gesch, Phys. Rev. B18 (1978) 794. P. Stallhofer, J.P. Kotthaus and G. Abstreiter Solid State Commun. 32 (1979) 655. K. Hatanaka, S. Onga, Y. Yasutada and S. Kawaji, Surface Sci. 73 (1978) 170. K. von Klitzing, Th. Englert. G. Landwehr and G. Dorda, Solid State Commun. 24 (1977) 703. J. Wakabayashi, K. Hatanaka and S. Kawaji, in: Proc. 14th Intern. Conf. on the Physics of Semiconductors, Edinburgh, 1978 (Institute of Physics, Conference series, No. 43, 1978) p. 1251. F.F. Fang and P.J. Stiles, Phys. Rev. 174 (1968) 823. L.M. Roth and P.N. Argyres, in: Semiconductors and Semimetals, Vol. I, Eds. R.K. Williardson and A.C. Beer ‘(Academic Press, New York, 1966) p. 159. H. Schlotterer, Solid State Electron 11 (1968) 947. S. Kawaji, K. Hatanaka, K. Nakamura and S. Onga, J. Phys. Sot. Japan 41 (1976) 1073. D.C. Tsui and G. Kaminski, Phys. Rev. Letters 42 (1979) 595. F.J. Ohkawa and Y. Uemura, Surface Sci. 58 (1976) 254. L.J. Sham and N. Nakayama, Surface Sci. 73 (1978) 272. R. Ktimmel, Z. Physik B22 (1975) 225. M.J. Kelly and L.M. Falicov,Phys. Rev. B15 (1977) 1974.
INVERSION LAYERS IN SILICON ON INSULAT~G
Th. ENGLERT
SUBSTRATES
and G. ~~~~
Hochfeldmagnetlabor Grenoble, France
Grenoble. Max-Planck-Institut fiir Festk&perforschung,
F-38042
J. PONTCHARRA Laboratoire d’Electronique
et de Technologie de I’lnformatique,
CENG, Grenoble, France
and G. DORDA Fors~hungs~borato~.en
der Siemens AG, ~~~~hen,
Germany
Received 20 July 1979; accepted for publication 5 September 1979
Magnetoconductance oscillations in silicon MOSFETs on sapphire and spine1 substrates were studied in magnetic fields up to 20 Tesla. For (100) n-type inversion layers the cyclotron mass and the effective Land& g-factor were determined from a measurement of the temperature dependence and the variation of the oscillatory structure in a tilted magnetic field. Apart from the unexplained valley degeneracy factor of two the results are in good agreement with the conception that due to the built-in stress the I?; subband is occupied. The Land&g-factor obtained is about the same as in MOSFETs grown on bulk material. The occurrence of a beat effect in the oscillations above about 12 Tesla in silicon on sapphire samples can be explained by a splitting of the ground subband of about 1 meV. This effect was not observed on silicon on spine1 samples which favours an explanation based on the stress anisotropy in silicon on sapphire.
1. Introduction
The physical properties of an electron gas in the surface space charge layer of semiconductors have been the subject of considerable theoretical and experimental work during the last years. Silicon field effect transistors (FET) of the MOS-type (Metal-Oxide-Semiconductor) provide a readily available tool for the study of surface quantization which arises from the restriction of the carrier motion in the direction perpendicular to the surface [ 11. Among all possible surface orientations MOSFETs grown on a (100) surface of silicon exhibit the best device characteristics. In the SOS technology (silicon on sapphire or spinel) thin expitaxial layers of silicon on single crystal sapphire or spine1 substrates are used for the fabrication of 427
MOSFETs. Thii technology has been developed in order to improve some device properties, like e.g. the switching time. However, the mobility of SOS MOS devices is in general lower than that of conventional MOSFETs. One reason is the existence of traps at the interface between the insulating substrate and the silicon film. A more fu~damen~l difference, which makes the system attractive from the physical point of view, is due to the presence of large lateral stresses in the silicon film, This stress builds up when the wafers are cooled down from the growth temperature to room temperature. From the different thermal expansion coefficients of silicon and sapphire a stress of 9.2 kbar at room temperature has been calculated 121. Recently we have determined the stress in our devices experimentally using Raman spectroscopy and obtained a value of 8.7 kbar at 77 K. Details of the experiment are described elsewhere [3]. The built-in stress changes the electronic structure of the surface charge layer significantly. In the case of an n-type inversion layer on a (100) silicon surface the six degenerate conduction band minima are split into two quasi two-~ensior~al subband systems Ei and Ej.In the absence of stresses the energetically lowest subband is the E, band which consists of states o~~nating from the two valleys with a large effective mass perpendicular to the surface. The theoreticai cyclotron mass in the Ee band is 0.19 nao. The next higher subband, EA is fourfold degenerate with a mass of 0.42 mo. The energy difference EA - E. is of the order 20 meV depending on the surface electric field strength. In the presence of stresses the E(k) minima are shifted relative to each other. Using the deformation potential constant of bulk silicon one finds that a compressional stress of 8.7 kbar, which is isotropic parallel to the surface, leads to splitt.ing of the E. and EL subband by about 80 meV. As a consequence the energetically lowest subband in the SOS system should be the Eb subband with a valley degeneracy of 4 and a theoretical cyclotron mass of 0.42 PYle. The occupation of the Ek subband could be observed on conventions (100) MOSFETs in measuren~ent of the surface quantum oscitiations of the ShubnikovDe Haas type (SdH) under external unaxial pressure [4] and recently in cyclotron resonance experiments on the same system [5]. The first measurements of SdH oscillations on SOS samples were published by Hatanaka et al. f6]. They reported a measured cyclotron mass varying between 0.3 and 0.4 m. and a valley degeneracy of 4. However, it could be demonstrated in tilted field experiments f7] that the observed valley degeneracy is only two. The effective mass was estimated to be 0.5 m, f 10% f7f. In a more recent pub~cat~on Wakabayashi et al. [8] also reported the observation of a valley degeneracy factor of 2 and an effective mass varying from 0.6 to 0.5 m. for different carrier concentrations. However, in this paper a different alignment of the observed SdH peaks is used and consequently unusually large values for the Land6 g-factor are proposed. Zn order to get additional information we have performed measurements in magnetic fields up to 19.5 T. We have turned the samples in the magnetic field to determine the Land6 g-factor. Since the maximum carrier mobility for SOS devices at
low temperature is only of the order 1000 cm2/V 1s high magnetic fields are indispensable for such experiments. We have studied an interference effect which occurs above about 12 T in silicon on sapphire samples. A comparison is made between the properties of silicon on sapphire and silicon on spine1 devices.
2. Experimentaf Silicon on sapphire samples f(lOO) Sif(iOl2) sapphire) were provided by the Forscl~ungs~borato~en der Siemens AG, Munchen, and by the Laboratoire d’Electronique et de Technologie de l’Informatique, CENG, Grenoble. The samples had a short, broad channel, the oxide thickness was 1200 A. Silicon on spine1 samples {(loo) Si/(lOO) spinel} were provided by Siemens, Miinchen. The thickness of the silicon layer varied from 0.6 to 0.8 pm. The SdH oscillations were ~vestigated using standard DC and AC modula~on techniques for the measurement of the conductivity or its derivative do/d V,
3. Ex~r~entaI
results
3.1. Silicon on sapphire For the measurement of the spin splitting and for a determination of the valley degeneracy it is essential to know the energy level scheme which belongs to the observed oscillatory structure. Since the first experiments of Fang and Stiles 191, the tilted field method has proved to be very succesful for a determina~on of the ratio between spin splitting g&B 4’g: Land& factor, fin: Bohr’s magneton) and the Landau splitting kw, (oc: cyclotron frequency eB[m,). Because of the restriction of the carrier motion essentially parallel to the surface in a quasi two-dimensional system the Landau splitting depends only on the component of the magnetic field perpendicular to the surface whereas the total magnetic field determines the spin splitting. Fig. 1 shows some recordings of quantum oscillations as a function of the gate voltage for different angles 9, r$ being the angle between the magnetic field and the surface normal. In this experiment the magnetic field perpendicular to the surface, BL, was kept constant. When the sample was tilted by an angle Q the total magnetic field Br, was increased so that B1 =Btot cos $ remained constant. In such an exper~ent the spin spotting increases proportions to I/cos $Jwhereas the Landau splitting does not change. A relative maximum of the oscillations is expected when the ratio of spin splitting to Landau splitting gm,/(2wa0 CDScb>= z, z being an integer. In these cases spin split levels of different Landau quantum numbers coincide. A doubling of the SdH frequency and a relative minimum of the amplitude occurs when gm,/f2mo cos @) = z t $; We observed a relative maximum of the
Th. Englert et al. ~~n~e~si~nZayers in .Sion instating ~~st~ntes _~~~~~ ~_.. ---_____- ~~-_
,
SOS EL= 10.5T
8~18.3
T
Fig. 1. Quantum oscillations on a silicon on sapphire device at different tilt angles #_ The magnetic field perpendicu~r to the surface is constant. Fig. 2. Quantum oscillations on a silicon on sapphire device at different tilt angles c$.The total magnetic field is constant.
oscillations at 35” and a minimum at 57” for a carrier concentration of n - 1.5 X 1012 cme2. Fig. 2 shows recordings at higher tilt angles. In this case a constant magnetic field of B = 18.3 T was applied perpendicul~ to the surface. Above about 60” the two Ievels indicated by arrows begin to merge and a second coincidence is observed forqb=65”. From the observation of three consecutive integer or half integer coincidences we obtain PC 2m0 cos 35” =’ ’
mc 2m0 cos 57”
=z+;,
gmC
2m0 cos 65”
=z+l.
The ratio of these values is 1 : 1.50 : 1.94. It follows that z = 1. Therefore the ratio of spin splitting to Landau splitting at @= 0 isgm,/2m0 = 0.82 for a carrier density of pa- 1.5 X 1012 cm-‘. This means that the observed minima in the SdH oscillations of the conducti~ty occur between spin split levels of the same Landau quantum number. Spin split levels of adjacent Landau levels overlap. The Landau level scheme proposed by Wakabayashi et al. [8] uses z = 2 for the first observed coincidence. This is, however, not compatible with our data. The width of the first observed peak is only about half as large on the gate voltage scale as that of the subsequent peaks. This results from the different degeneracy factor of the lowest
Th. Englert et al. /Inversion
layers in Si on insulating substrates
431
level and is consistent with our level scheme OJ, OtlJ, 1?2$ etc. (t, 4 denotes the spin orientation). The valley degeneracy was found to be 1.85 + 10% in agreement with former results [7,8]. The discrepancy between the theoretically expected value of 4 and the experimental results will be discussed later. From the temperature dependence of the amplitude (A) of the SdH oscillations as a function of the magnetic field the cyclotron mass was determined. Using the formula A a T/sinh(2n2kT/Ao,)
,
we obtained the values given in table 1. These values are in agreement with an estimate made in our previous publication [7] and with the data of Wakabayashi et al. [8] in their more recent publication. The relatively large error margin which we assumed will be discussed later. The cyclotron mass is larger than expected from effective mass theory for the EA subband. However, similar mass values have been observed in SdH measurements on bulk (100) MOSFETs under unaxial external stress when the Ei subband was occupied [4]. In recent cyclotron resonance experiments on the same system a value of 0.48 m, independent of the carrier concentration was obtained [5]. The enhanced cyclotron mass in the EA subband has not yet been explained theoretically. From the measurements of gm,/2m0 and the cyclotron mass m, a Land6 g-factor g - 3 is deduced at n - 1.5 X 1012 cme2. This value is comparable to the g-factor obtained in the &, subband. Unexpected interference effects occur above about 12 T when the SdH oscillations are measured as a function of the magnetic field. Fig. 3 shows typical results for the derivative dI/dV, at three different gate voltages. The underived curve is also plotted in the case of V, = 11 V. A rather complicated oscillatory structure is observed when the surface quantum oscillations are measured at a high magnetic field as a function of the gate voltage. This can be seen in the lower part of fig. 4. In fig. 5 the magnetic field position of the SdH extrema are plotted as a function of the gate voltage. The occurrence of the beat effect is indicated by arrows. It is most pronounced at relatively small gate voltages. Only some of the points in fig. 5 lie on straight lines with a common intercept. It should be mentioned that this effect has
Table 1 Cyclotron
mass mJmo
at various electron
n (cme2)
m&no
1.4 2.3 3.5 4.4
0.51 0.49 0.52 0.47
x X x x
10’2 1Ol2 10’2 10’2
(i 10%)
concentrations
n
Th. Englert et al. /Inversion
SILICON
ON
n-channel
SAPPHIRE
layers in Si on insulating substrates
1
(100)
r\
I
I
5
10
I 15 B(T)
Fig. 3. SdH oscillations
SILICON ON SAPPHIRE
I 20 -
on a silicon on sapphire
sample at different
gate voltages.
Fig. 4. Conductivity and field effect mobility for a silicon on sapphire part) and SdH oscillations (lower part) at a constant magnetic field.
sample
at B = 0 (upper
been observed for all our samples investigated even of different origin. Therefore it seems to be an’intrinsic property of the silicon on sapphire system. A possible explanation is the splitting of the ground subband Ei by a small anisotropy of the stress along the surface. Since the surface used for the expitaxy is not a plane of high symmetry, the different thermal expansion parallel and perpendicular to the c-axis of sapphire leads to an anisotropy of about 5% of the total built-in stress [2]. This should give rise to a stress induced valley splitting of about 5 meV. Unfortunately the stress anisotropy has not been determined experimentally up to now. In order to see whether such a splitting can account for the observed interference effect, we have performed a computer simulation by superimposing SdH oscillations from two valleys with slightly different Fermi energies. The SdH formula given by Roth et al. [lo] was employed because the two-dimensional nature of the electron gas was not significant. Use was made of the experimentally determined gm,/2m,, value. For a gate voltage of 11 V we were able to simulate the experimentally observed interference structure with a splitting of AE = 1 meV. Although
I
Th. Englert et al. /Inversion
r
SILICON
layers in Si on insulating substrates
ON
433
SAPPHIRE
20
t m 15
10
5
5
10
15
20
25
30
35
Fig. 5. Extrema of SdH oscillations for a silicon on sapphire MOSFET. The arrows indicate the occurrence of interference effects.
this splitting is considerably smaller than expected from the calculated anisotropy of the stress it can explain the results qualitatively. The interference effect has some consequences for the interpretation of SdH data at lower magnetic fields. Although it can only be resolved above about 12 T it changes the shape and the amplitude of the oscillations at much lower fields. This causes an error in the determination of the effective mass from the temperature dependence of the SdH amplitude using only one fundamental period. In order to estimate this error we have simulated SdH oscillations for Vs = 11 V as described above at various temperatures. For the calculation we used the theoretical mass value m, = 0.43 mo. Then we have recalculated the cyclotron mass from the temperature dependence of the simulated curves using the formula A a T/sinh(2~2kT/Ao,)
.
We found a discrepancy of about 5% between this result and the value inserted in the calculation. Therefore we assumed a rather large error margin for our mass data shown in table 1. 3.2. Silicon on spine1 As for the amount of built-in stress the system (100) silicon on (100) spine1 is very similar to silicon on sapphire [ 111. However, in this case the stress should be isotropic parallel to the film surface because spine1 is cubic. Therefore a comparison
434
Th. Englert et al. j Inversion layers in Si on inflating castrates
1
t
L___
SILICON
ON
SPINEL
I
I
I
I
5
10
15
20
B(T)
--+
Fig. 6. SdH oscillations on a silicon on spine1 sample.
of the properties of MOSFETs grown on the two different insulating substrates is a good check for the model proposed above. Fig. 6 shows the SdH oscillations as a function of the magnetic field for different gate voltages. The extrema are plotted versus gate voltage in fig. 7. As can be seen from the data, there is no anomalous structure in the oscillations. Especially the beat effect which was observed for
20
SILICON
ON
SPINEL
T i= m
5
10
15
20
25 vg w
30 --b
Fig. 7. Extrema of SdH oscillations for a silicon on spine1 device.
Th. Englert et al. /Inversion
layers in Si on insulating substrates
435
silicon on sapphire samples does not exist. This confirms our model that the anisotropy of the stress is responsible for the splitting. We have found another difference in the properties of silicon on sapphire and silicon on spine1 devices. When the field effect mobility of MOSFETs on sapphire substrate is measured at low temperatures (below 80 K) a minimum is observed at a carrier density of about 4.4 X 10” cm -2. This structure has been reported first by Kawaji et al. [ 121 and interpreted as the occupation of the E,-, subband with a small effective mass. However, the energy difference Ee - Eh calculated from the stress values seems to be too large for an occupation at these carrier densities. We observed such a minimum in the field effect mobility on all our sapphire samples. There was no indication for the occupation of another subband in our SdH data. It should be mentioned, however, that the oscillations at high gate voltages are rather weak (see e.g. fig. 5). For our silicon on spine1 samples no such structure in the field effect mobility could be observed. We have no satisfactory explanation for the effect at present but this different behaviour seems to be important for any future interpretation.
4. Discussion and concluding
remarks
We have checked in this paper that the ground state of a (100) inversion layer on silicon on sapphire is twofold degenerate. The cyclotron mass and the effective g-factor have been determined. Apart from the valley degeneracy problem the results are in agreement with the conception that due to the built-in stress the EA subband is occupied. An additional splitting of the subband was detected in the SdH oscillations at high magnetic fields which can be explained qualitatively by the anisotropy of the stress parallel to the surface. This model is supported by the results on silicon on spine1 samples where no such anisotropy exists. In our discussion we have neglected so far the discrepancy between the theoretically expected and the observed valley degeneracy. It should be mentioned that this problem is not limited to the SOS system. It has been a serious difficulty in understanding the physics of surface space charge layers on silicon of the orientation (110) and (111). However, a valley degeneracy of six for specially treated (111) samples was observed recently by Tsui et al. [ 131’. This shows that a valley degeneracy factor larger than two is possible. Since the samples used in that experiment were fabricated in a different way, one has to assume that some property of the interface which is not known up to now leads to the lifting of the valley degeneracy In this paper we have explained the observed splitting of the ground subband in silicon on sapphire devices by the anisotropy of the stress in the surface. Attempts to interpret the beat effect by two periods caused by valley splitting does not seem reasonable for various reasons. First of all, it is difficult to see, how valley splitting can arise, if the “tunneling in k-space” [ 181 or the “surface scattering” [ 191 models
Th. Englert et al. /Inversion
436
layers in Si on insulating substrates
of the valley splitting are invoked. Moreover, the experimentally observed splitting is not compatible with the electric field dependence of the valley splitting as theoretically predicted [ 14-161. The most convincing argument is, however, that the splitting is missing in the silicon-on-spine1 devices, However, the proposed model has some implications. The stress anisotropy can only split those E(k) valleys which are located at right angles in k-space in the stress-free case. If the two occupied valleys were on the same axis. uniaxial stress should have no effect at all. It should be noted that the model of Kelly and Falicov [17] which leads to a reduction of the valley degeneracy is based on the interaction of electrons in valleys perpendicular to each other. At present the charge density wave model [17] could neither be proved nor disproved. One argument against its validity has been the invoked strength of the intervalley electron-electron interaction, which must be much larger than in bulk silicon.
References [l] [2] [3] [4] [5] [6] [7] [8]
[9] [lo] [l l] [12] [13] [14] [15] [16] [17]
See e.g., G. Landwehr, in: Solid State Devices, 1978, Eds. M. Savelli and J.P. Nougier (Les Editions de Physique, Orsay, 1979) p. 1. A.J. Hughes and A.C. Thorsen, J. Appl. Phys. 44 (1973) 2304. Th. Englert and G. Abstreiter, Solid State Electron. 23 (1980) 31. Th. Englert, G. Landwehr, K. van Klitzing, G. Dorda and H. Gesch, Phys. Rev. B18 (1978) 794. P. Stallhofer, J.P. Kotthaus and G. Abstreiter Solid State Commun. 32 (1979) 655. K. Hatanaka, S. Onga, Y. Yasutada and S. Kawaji, Surface Sci. 73 (1978) 170. K. von Klitzing, Th. Englert. G. Landwehr and G. Dorda, Solid State Commun. 24 (1977) 703. J. Wakabayashi, K. Hatanaka and S. Kawaji, in: Proc. 14th Intern. Conf. on the Physics of Semiconductors, Edinburgh, 1978 (Institute of Physics, Conference series, No. 43, 1978) p. 1251. F.F. Fang and P.J. Stiles, Phys. Rev. 174 (1968) 823. L.M. Roth and P.N. Argyres, in: Semiconductors and Semimetals, Vol. I, Eds. R.K. Williardson and A.C. Beer ‘(Academic Press, New York, 1966) p. 159. H. Schlotterer, Solid State Electron 11 (1968) 947. S. Kawaji, K. Hatanaka, K. Nakamura and S. Onga, J. Phys. Sot. Japan 41 (1976) 1073. D.C. Tsui and G. Kaminski, Phys. Rev. Letters 42 (1979) 595. F.J. Ohkawa and Y. Uemura, Surface Sci. 58 (1976) 254. L.J. Sham and N. Nakayama, Surface Sci. 73 (1978) 272. R. Ktimmel, Z. Physik B22 (1975) 225. M.J. Kelly and L.M. Falicov,Phys. Rev. B15 (1977) 1974.